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same topic. Gauss' official report to the Philosophical Faculty
of the University of Gottingen is noteworthy as one of the rare
formal pronouncements hi which Gauss let himself go.
'The dissertation submitted by Herr Riernann offers con-
vincing evidence of the author's thorough and penetrating
investigations in those parts of the subject treated hi the disser-
tation, of a creative, active, truly mathematical mhid, and of a
gloriously fertile originality. The presentation is perspicuous
and concise and, in places, beautiful. The majority of readers
•would have preferred a greater clarity of arrangement. The
whole is a substantial, valuable work, which not only satisfies
the standards demanded for doctoral dissertations, but far
exceeds them/
A month later Riemann passed his final examination, in-
cluding the formality of a public 'defence' of his dissertation.
All went oft successfully, and Riemann began to hope for a posi-
tion hi keeping with his talents. 4I believe I have improved my
prospects with my dissertation", he wrote to his father; *I hope
also to learn to write more quickly and more fluently in time,
especially if I mmgle hi society and if I get a chance to give
lectures; therefore am I of good courage.' He also apologizes to
his father for not having gone after a vacant assistantship at the
Gottingen Observatory more energetically, but as he hopes to
be 'habilitated' as a Privatdozent the outlook is not as dark as
it might be.
For his Hdbilitationsschrift (probationary essay) Biemann
had planned to submit a memoir on trigonometric series
(Fourier series). But two and a half years were to pass before he
might hang out his sign as an unpaid university instructor
picking up what he could in the way of fees from students not
bound to attend his lectures. During the autumn of 1852 Rie-
mann profited by Dirichlet's presence hi Gottingen on a vaca-
tion and sought his advice on the embryonic memoir, Rie-
mann's friends saw to it that the young man met the famous
mathematician from Berlin - second only to Gauss - socially.
Dirichlet was captivated by Riemann's modesty and genius,
*Next morning [after a dinner party] Dirichlet was with me for
two hours,* Riemaun wrote his father. 'He gave me the notes